最好是一些能举一反三类的题目

1.X和y是自然数,规定小x*y=4X-3y,如果5*a=8,那么a是几?
a=（4*5-8）/3
=4
2.某班一次集合,请假人数是出席人数的1/9,中途又有一人请假离开,这样一来请假人是出席人数的3/22,那么这个班共有多少人?
设第一次请假人为X,则出席人数为9X
（9X-1）*（3/22)=x+1
x=5
所以：总人数为5+9*5=50（人）
3.8又4分之3-0.35+（1又4分之1-6又20分之13）
=8又3/4-7/20+1又1/4-6又13/20
=（8又3/4+1又1/4）-（7/20-6又13/20）
=3
4.1/2*3 +1/3*4 +1/4*5.+1/49*50
=1/2-1/3+1/3-1/4+1/4-1/5+.+1/49-1/50
=1/2-1/50
=12/25
5.1/1*3+1/3*5+1/5*7+.+1/47*49
=(1-1/3+1/3-1/5+1/5-1/7+.+1/47-1/49)*1/2
=(1-1/49)*1/2
=48/49*1/2
=24/49
6.1/2*5+1/5*8+1/8*11+.+1/20*23
=(1/2-1/5+1/5-1/8+1/8-1/11+.+1/20-1/23)*1/3
=(1/2-1/23)*1/3
=21/46*1/3
=7/46
7.1又13+7/12-9/20+11/30-13/42
=1又1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7
=1又2/3-1/7
=1又11/21
8.2003/1*3+2002/3*5+2002/5*7+2002/7*9+2002/9*11
=（1/1*3 *2002 +1/3*5 *2002 +1/5*7 *2002 +1/9*11 *2002）*1/2
=（1-1/3+1/3-1/5+1/5-1/7+1/9-1/11）*2002*1/2
=（1-1/11）*2002*1/2
=10/11*2002/2
=9109.1/2+1/4+1/8+1/16+1/32
=（1/2+1/4+1/8+1/16+1/32+1/32）-1/32
=1-1/32
=31/32 10.1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/3-1/4+1/4-1/5+1/5-1/6.+1/9-1/10
=1/3-1/10
=7/30
11.1-1/4+1/20+1/30+1/42+1/56
=1-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8
12.1/1*5+1/5*9+1/9*13+.+1/55*59
=(1-1/5+1/5-1/9+1/9-1/13+.+1/55-1/59)*1/4
=(1-1/59)*1/4
=29/118
13 .(1+1/3+1/5+1/7)*(1/3+1/5+1/7+1/9)-(1+1/3+1/5+1/7+1/9)+(1/3+1/5+1/7)
设(1+1/3+1/5+1/7)为a,（1/3+1/5+1/7）为b
a*(b+1/9)-(a+1/9)*b
=ab+1/9a-ab-1/9b
=1/9*(a+b)
=1/9
14.5/14*5/6-7/12*5/14+9/20*5/14
=5/14*(5/6-7/12+9/20)
=5/14*[1/2+1/3-(1/3+1/4)+1/4+1/5]
=5/14* (1/2+1/3-1/3-1/4+1/4+1/5)
=5/14*7/10
=1/4
15.1/3+1/15+1/35+1/63+1/99
=1/1*3 +1/3*5 +1/5*7 +1/7*9 +1/9*11
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)*1/2
=(1-1/11)*1/2
=5/11